Question

After all foreign and U.S. taxes, a U.S. corporation expects to receive 2 pounds of dividends per share from a British subsidiary this year. The exchange rate at the end of the year is expected to be $1.29 per pound, and the pound is expected to depreciate 5% against the dollar each year for an indefinite period. The dividend (in pounds) is expected to grow at 10% a year indefinitely. The parent U.S. corporation owns 10 million shares of the subsidiary. What is the present value in dollars of its equity ownership of the subsidiary? Assume a cost of equity capital of 11% for the subsidiary.

Answer 1

Answer:

Expected Dividend per share in pounds = £ 2

The exchange rate at the end of the year is expected to be $1.29 per pound

Expected Dividend per share in US $ = 2 * 1.29 = $2.58

U.S. Corporation owns 10 million shares of the subsidiary

Expected Dividend of its equity ownership in US $ = 10 * 2.58 = $25.80 million

Present value in dollars of its equity ownership of the subsidiary = Expected Dividend per share in US $ / (cost of equity - (Dividend growth rate - Pound depreciation rate))

= 25.80 / (11% - (10% - 5%))

= $430 million

Present value in dollars of its equity ownership of the subsidiary = $430 million

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Alternate formula:

Rate of growth net exchange depreciation = ((1 + Growth rate) / (1 + Exchange rate depreciation)) - 1

= ((1 + 10%) / (1 + 5%)) - 1

= 4.76190476190477%

Present value in dollars of its equity ownership of the subsidiary = Expected Dividend per share in US $ / (cost of equity - growth rate net of exchange rate depreciation)

= 25800000 / (11% - 4.76190476190477%)

= $413587786.26

Or $413,587,786

Present value in dollars of its equity ownership of the subsidiary = $413,587,786